Sedimentation of a rigid helix in viscous media

Abstract

We consider sedimentation of a rigid helical filament in a viscous fluid under gravity. In the Stokes limit, the drag forces and torques on the filament are approximated within the resistiveforce theory. We develop an analytic approximation to the exact equations of motion that works well in the limit of a sufficiently large number of turns in the helix (larger than two, typically). For a wide range of initial conditions, our approximation predicts that the centre of the helix itself follows a helical path with the symmetry axis of the trajectory being parallel to the direction of gravity.The radius and the pitch of the trajectory scale as non-trivial powers of the number of turns in the original helix. For the initial conditions corresponding to an almost horizontal orientation of the helix, we predict trajectories that are either attracted towards the horizontal orientation, in which case the helix sediments in a straight line along the direction of gravity, or trajectories that form a helical-like path with many temporal frequencies involved. Our results provide new insight into the sedimentation of chiral objects and might be used to develop new techniques for their spatial separation. * alexander.morozov@ed.ac.uk 1 arXiv:1811.08491v1 [physics.flu-dyn]

Helical trajectories of swimming cells with a flexible flagellar hook

“…Although it has been observed in generic settings that a helical flagellum does not substantially deform under rotation [14], a more recent investigation by Jabbarzadeh & Fu indicates that both hook as well as flagellum deformability is needed to account for the large hook angles seen in such flicks [15,16], consistent with experimental observations [13]. Even without the added complexity of a cell body, the chirality of a helical filament results in coupling of translation and rotation which can lead to surprisingly rich dynamics under gravity [17], under magnetic actuation [18,19], near surfaces [20,21], in a background flow [22,23] or even double-helical trajectories for double-helical "superhelices" like insect spermatozoa [24,25]. For very soft filaments, other instabilities and dynamics abound [26][27][28] The end result of such flagellar activity is the body trajectory, itself an object of intense scrutiny.…”

Helicoidal particles and swimmers in a flow at low Reynolds number

“…Another important extension is to include gravity effects. Even a simple helix generates a complex trajectory under gravity (Kim & Rae 1991;Palusa et al 2018), and simple director equations will be very useful considering the dynamics in a flow.…”

Phoretic self-propulsion of helical active particles

“…We have also sought to compare our results with resistive force theory (RFT), using the expressions in Palusa et al. (2018) and Chattopadhyay et al. (2006).…”

“…These findings have implications for the study of helix sedimentation dynamics (Palusa et al. 2018).…”